This invention pertains to using geophysical data in a joint inversion to infer geological properties of the subsurface. During an inversion, the aim is to minimize the difference between the measured data and the data predicted by the inversion model. In order to perform a predicted data calculation, geophysical parameters such as seismic velocity (or elastic coefficients), or electrical conductivity must be known. When multiple data types (e.g. reflection seismic and electromagnetic data) are inverted simultaneously, it is known as a joint inversion. Geophysical data are likely to include active seismic reflection data; active seismic refraction data; electromagnetic data (either controlled source or magneto-telluric); and/or gravity measurements; however, it may in addition include any other type of data that can be used to infer the properties of subsurface rocks in the region of interest.
Geophysical properties, such as elastic coefficients, density, and electrical conductivity, can be converted to the geological properties of interest in hydrocarbon exploration (e.g., porosity and fluid type) via rock physics relationships (obtained empirically or theoretically). In this way the different geophysical data types are linked in the joint inversion. These rock physics relationships can be embedded in a joint inversion of geophysical data. They are used to calculate the needed geophysical parameters (elastic coefficients, electrical conductivities, and density) that are necessary for forward calculating the predicted data. Using the forward predicted data, a misfit between the predicted and observed data is computed. The model is then iteratively updated using some optimization scheme to minimize the difference between predicted and measured data.
In general, to perform joint inversions of this type, one must assume a priori a particular rock physics relationship between the geophysical parameters (for example sonic velocity, shear wave velocity, density or conductivity) that predict the data and the geological parameters (for example porosity or water saturation) of interest. By assuming a rock physics relationship we are assuming a lithology and depositional environment present in the subsurface. A lithologic class is a rock type that is considered to possess unifying rock physics behavior for the purposes of the inversion; e.g., clastics and carbonates might be considered two distinct lithologic classes, each with their own rock physics relationship. However, the lithology in the subsurface of a particular region of interest is often not known beforehand, and further, a single physical volume sampled by the data may contain more than one lithology with an unknown spatial distribution of those lithologies.
One way to jointly invert multiple geophysical data for geophysical properties is to assume structural coupling (e.g., Haber and Oldenburg, 1997) where anomalies in one of the geophysical properties (e.g., velocity) are required to occur in the same location as anomalies in one or more of the other geophysical properties (e.g., resistivity). The problem with this approach is that it is highly nonlinear, when data of very different resolutions are being inverted. This makes it practically challenging to invert, for example, high frequency seismic data together with low frequency CSEM data.
A joint inversion for geophysical properties can also be performed by assuming explicit or implicit relationships between the parameters. For example two parameters can be assumed to be correlated (see for example Farquharson et al., 2010). The problem with this approach is that these relationships have to be known beforehand and must be adequate for the subsurface area of interest, or the inversion will fail.
In order to infer geological properties from an inversion for geophysical properties, a rock physics model can be used to convert the inverted geophysical properties into geological properties. Even though this approach allows one to infer geological properties, it relies on the inverted geophysical properties. The conversion does not rely on the measured data and thus does not allow for feedback between measured data and geological properties.
Doetsch et al. (2010) perform a joint inversion using structural coupling. Following the inversion, they analyze the inverted geophysical properties for patterns of similar properties, such as zones that are fast and resistive versus zones that are slow and conductive. These zones of similar geophysical properties are then treated as one model cell and they invert for average geophysical properties for each zone. In the next step they use the average properties to do an after-the-fact conversion to the average geological properties, using rock-physics relationships. The problem with this approach is that it relies on the data being of similar resolution due to the structural coupling. Furthermore, as described before, there is no feedback between the inferred average geological properties and the measured data. In general applications, therefore, this method may not succeed.
Another approach to joint inversion uses statistical methods. A lithology in these methods is simply defined as a class of rocks that can be assigned a probability density function (“pdf”) of continuous parameters (e.g. seismic p-wave velocity, or porosity)—no explicit rock physics equations are necessary. The use of the statistical method is, for example, demonstrated by Guillen et al (2004) who use gravity and magnetic data to invert for lithology of the subsurface; Buland et al. (2008) use a similar technique to invert for seismic reflection data. Unfortunately, this approach assumes that the pdf for each lithology is known beforehand, which is rarely the case for most exploration settings.
In another approach for joint inversion, the geologic environment is assumed known and the corresponding rock physics model is applied (see Abubakar et al., 2010; Jing et al., 2010; Hoversten, 2010). For example, if the lithology is assumed to be clastic, a clastic rock physics model is used to relate the velocity, density and resistivity to the rock properties (e.g., Vshale, porosity, Water saturation). This has the advantage that the geological parameters are inverted for directly, i.e., this approach allows for feedback between geologic parameters and the measured data. But unless the lithology is known beforehand, the assumption of a specific rock physics model can strongly bias the inverted result. For example, in the event the lithology is in fact a volcanic, such as basalt, and not clastic, the estimates of velocity and density will be incorrect and the characterization of rock in terms of Vshale will not make sense. That is, unless the lithology is known beforehand, the assumption of a specific rock physics model can strongly bias the inverted result, leading to incorrect results.
DiCaprio et al. (2010) present an approach that allows jointly inverting geophysical data for subsurface properties in cases where the lithology class is not known beforehand. Instead of assigning a rock type a priori, their invention prescribes using the lithology classes as a discrete inversion parameter to be found during the inversion. At each step in the inversion, the appropriate rock physics relationship is used on the resolution cells depending on what lithology they are currently assigned. The lithology parameter is allowed to vary both as the inversion evolves and as a function of space (allowing for mixed lithologies in a single physical volume). A drawback of this approach is that specialized optimization schemes must be used, and the model space is greatly expanded. This may not be computationally practical for all applications.
The invention presented here is an alternative approach to DiCaprio et al. (2010). It also allows for the inversion of geological properties in cases where the lithology is unknown. There is no restriction to use data of similar resolution. Instead of one inversion with additional parameters to be inverted for (DiCaprio et al, 2010), it uses different data coupling strategies in different stages of the inversion to arrive at a model of geological properties and lithologies.